Cell processes like endocytosis, membrane resealing, signaling and transcription involve conformational changes which depend on the chemical composition and the physicochemical properties of the lipid membrane. The better understanding of the mechanical role of lipids in cell membrane force-triggered and sensing mechanisms has recently become the focus of attention. Different membrane models and experimental methodologies are commonly explored. While general approaches involve controlled vesicle deformation using micropipettes or optical tweezers, due to the local and dynamic nature of the membrane, high spatial resolution atomic force microscopy (AFM) has been widely used to study the mechanical compression and indentation of supported lipid bilayers (SLBs). However, the substrate contribution remains unkown. Here, we demonstrate how pulling lipid tubes with an AFM out of model SLBs can be used to assess the nanomechanics of SLBs through the evaluation of the tube growing force (Ftube), allowing for very local evaluation with high spatial and force resolution of the lipid membrane tension. We first validate this approach to determine the contribution of different phospholipids, by varying the membrane composition, in both one-component and phase-segregated membranes. Finally, we successfully assess the contribution of the underlying substrate to the membrane mechanics, demonstrating that SLB models may represent an intermediate scenario between a free membrane (blebs) and a cytoskeleton supported membrane.